Value-added in higher education: ordinary least squares and quantile regression for a Colombian case (2017)
Colombia applies two mandatory National State tests every year. The first, known as Saber 11, is applied to students who finish the high school cycle, whereas the second, called Saber Pro, is applied to students who finish the higher education cycle. The result obtained by a student on the Saber 11 exam along with his/her gender, and socioeconomic stratum are our independent variables while the Saber Pro outcome is our dependent variable.We compare the results of two statistical models for the Saber Pro exam. The first model, multi-lineal regression or ordinary least squares (OLS), produces an overall well fitted result but is highly inaccurate for some students. The second model, quantile regression (QR), weight the population according to their quantile groups. OLS minimizes the errors for the students whose Saber Pro result is close to the mean (a process known as estimation in the mean) while QR can estimate in the -quantile for every . We show that QR is more accurate than OLS and reveal the unknown behavior of the socioeconomic stratum, the gender, and the initial academic endowments (estimated by the Saber 11 exam) for each quantile group.